An efficient implementation of the high-fidelity generalized method of cells for complex microstructures

The high-fidelity generalized method of cells (HFGMC) enables micromechanical analysis of heterogeneous materials with high accuracy but does so at the cost of computational efficiency. In this paper, an implementation of the triply periodic HFGMC is developed to enable high-resolution simulations of materials with complex microstructures at a significantly reduced computational cost. This paper describes efficient reformulation and develops low-cost algorithms to reduce overall computation time and memory required to analyze complex 3D microstructures. The low-cost algorithms exploit the sparsity of the data by storing and performing calculations on only the non-zero values. The Parallel Direct Sparse Solver (PARADISO) subroutine is used to execute the most computationally intensive processes in parallel on multiple cores. Simulations of two selected test cases demonstrate the validity, computational efficiency, and value of the developed implementation. The results indicate that the savings in computation time and required memory are substantial and more than 100 times in some cases. In addition, parallel processing further reduces the computation time. The efficiency achieved through this work makes the high-resolution simulation of complex microstructures using HFGMC for the prediction of accurate local stress/strain fields computationally feasible.